A first principle one‐dimensional (1‐D) dynamic model for tubular solid oxide fuel cell (SOFC) is developed. To convert the distributed model into a control relevant nonlinear state space model, an approximate analytical solution for reacting gas‐flow problem is proposed, and applied to the 1‐D SOFC dynamic model. Compared to numerical solutions, the proposed solution can significantly reduce requirements in computation, and thus, facilitate dynamic simulations and control applications. Distributed dynamic relations between current density and electromotive force (EMF) are investigated. Diffusion, inherent impedance, primary flow, heat transfer, and internal reforming/shifting reaction are considered simultaneously. Dynamic responses of the interested variables when external current, fuel and air inlet streams are perturbed by step changes are investigated through simulations. © 2008 American Institute of Chemical Engineers AIChE J, 2008.

Two studies compared hemispatial bias for perceiving chimeric faces in patients having either atypical or typical depression and healthy controls. A total of 245 patients having major depressive disorder (MDD) or dysthymia (164 with atypical features) and 115 controls were tested on the Chimeric Faces Test. Atypical depression differed from typical depression and controls in showing abnormally large right hemisphere bias. This was present in patients having either MDD or dysthymia and was not related to anxiety, physical anhedonia, or vegetative symptoms. In contrast, patients having MDD with melancholia showed essentially no right hemisphere bias. This is further evidence that atypical depression is a biologically distinct subtype and underscores the importance of this diagnostic distinction for neurophysiologic studies.

Formal inference in randomized clinical trials is based on controlling the type I error rate associated with a single pre-specified statistic. The deficiency of using just one method of analysis is that it depends on assumptions that may not be met. For robust inference, we propose pre-specifying multiple test statistics and relying on the minimum p-value for testing the null hypothesis of no treatment effect. The null hypothesis associated with the various test statistics is that the treatment groups are indistinguishable. The critical value for hypothesis testing comes from permutation distributions. Rejection of the null hypothesis when the smallest p-value is less than the critical value controls the type I error rate at its designated value. Even if one of the candidate test statistics has low power, the adverse effect on the power of the minimum p-value statistic is not much. Its use is illustrated with examples. We conclude that it is better to rely on the minimum p-value rather than a single statistic particularly when that single statistic is the logrank test, because of the cost and complexity of many survival trials.

The conventional approach to hypothesis testing for formal inference is to prespecify a single test statistic thought to be optimal. However, we usually have more than one test statistic in mind for testing the null hypothesis of no treatment effect but we do not know which one is the most powerful. Rather than relying on a single p-value, combining p-values from prespecified multiple test statistics can be used for inference. Combining functions include Fisher's combination test and the minimum p-value. Using randomization-based tests, the increase in power can be remarkable when compared with a single test and Simes's method. The versatility of the method is that it also applies when the number of covariates exceeds the number of observations. The increase in power is large enough to prefer combined p-values over a single p-value. The limitation is that the method does not provide an unbiased estimator of the treatment effect and does not apply to situations when the model includes treatment by covariate interaction.

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